197 Degree Angle

A 197° angle is reflex because it measures between 180° and 360°. It is the "outside" of a 163° angle: together they make a full 360° circle.

197° is 197/360 of a full circle, or 197π/180 radians. If you face north and turn 197° clockwise, you end up facing between S and SSW (closest to south-southwest (SSW)).

197° angle facts

Trigonometric values of 197°

197° on a protractor

How to draw a 197° angle with a protractor

1. Subtract from 360°: 360° − 197° = 163°. A standard protractor only goes to 180°, so you draw the smaller angle first.
2. Draw a straight line with a ruler and mark the vertex at one end.
3. Place the protractor's center mark on the vertex, line up the 0° baseline with your line, and make a dot at 163°.
4. Join the vertex to the dot. The inside angle is 163°; the outside angle, going the long way around, is 197°. Draw the angle arc on the outside and label it 197°.
5. With a 360° protractor you can skip the subtraction: put 0° on your first line and mark 197° directly.

Drawing it a 197° angle without a protractor (rise and run method)

1. 197° = 180° − 17°. Draw a straight line, pick a vertex on it, and build a 17° angle on one side as follows; the angle on the other side of the new line is 163°.
2. Draw a straight baseline and measure exactly 10 inches along it from the vertex.
3. At the 10-inch mark, draw a short line straight up at 90° (use a carpenter's square or the corner of a sheet of paper).
4. Measure 3.06 inches (about 3 1/16″) up that line and make a mark.
5. Join the mark to the vertex. The angle at the vertex is 17°, because tan 17° ≈ 0.3057.
6. That gives you 163°. The outside (reflex) angle is 197°.

Where you see 197° angles

• The Earth turns 197° on its axis in about 13 h 8 min.
• A 197° reflex angle is what you measure when you go the "long way" around, like the outside corner of a building or a turn of more than half a circle.

Related angles

• Explement: 163°
• 30°
• 45°
• 60°
• 90°
• 120°
• 135°
• 180°